Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #12 Jul 20 2022 10:11:28
%S 4,40,184,496,1240,2144,4380,6720,10860,15528,24300,30152,46036,57496,
%T 75056,96416,129052,148512,198392,225240,279576,336272,415988,453376,
%U 565052,648008,754808,848664,1026040,1085536,1331532,1452704,1652684,1862600,2084888,2247568,2662092,2887944,3193744
%N Number of regions formed in a square by straight line segments when connecting the n+1 points along each edge that divide it into n equal parts to the n+1 points on the edge on the opposite side of the square.
%C This sequence is similar to A355798 but here the corner vertices of the square are also connected to points on the opposite edge.
%H Scott R. Shannon, <a href="/A355838/a355838.jpg">Image for n = 2</a>.
%H Scott R. Shannon, <a href="/A355838/a355838_1.jpg">Image for n = 3</a>.
%H Scott R. Shannon, <a href="/A355838/a355838_2.jpg">Image for n = 4</a>.
%H Scott R. Shannon, <a href="/A355838/a355838_3.jpg">Image for n = 5</a>.
%H Scott R. Shannon, <a href="/A355838/a355838_4.jpg">Image for n = 6</a>.
%H Scott R. Shannon, <a href="/A355838/a355838_5.jpg">Image for n = 7</a>.
%H Scott R. Shannon, <a href="/A355838/a355838_6.jpg">Image for n = 8</a>.
%H Scott R. Shannon, <a href="/A355838/a355838_7.jpg">Image for n = 11</a>.
%H Scott R. Shannon, <a href="/A355838/a355838_8.jpg">Image for n = 16</a>.
%F a(n) = A355840(n) - A355839(n) + 1 by Euler's formula.
%Y Cf. A355839 (vertices), A355840 (edges), A355841 (k-gons), A355798 (without corner vertices), A290131, A331452, A335678.
%K nonn
%O 1,1
%A _Scott R. Shannon_, Jul 18 2022